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RESEARCH PAPERS

A Steepest-Ascent Method for Solving Optimum Programming Problems

[+] Author and Article Information
A. E. Bryson

Division of Engineering and Applied Physics, Harvard University, Cambridge, Mass.

W. F. Denham

Missiles & Space Division, Raytheon Company, Bedford, Mass.

J. Appl. Mech 29(2), 247-257 (Jun 01, 1962) (11 pages) doi:10.1115/1.3640537 History: Received September 06, 1961; Online September 16, 2011

Abstract

A systematic and rapid steepest-ascent numerical procedure is described for solving two-point boundary-value problems in the calculus of variations for systems governed by a set of nonlinear ordinary differential equations. Numerical examples are presented for minimum time-to-climb and maximum altitude paths for a supersonic interceptor and maximum-range paths for an orbital glider.

Copyright © 1962 by ASME
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